हिंदी

The Number of Permutations of N Different Things Taking R at a Time When 3 Particular Things Are to Be Included Isn − 3pr − 3,N − 3pr,Npr − 3,R ! N − 3cr − 3

Advertisements
Advertisements

प्रश्न

The number of permutations of n different things taking r at a time when 3 particular things are to be included is

विकल्प

  • n − 3Pr − 3

  •  n − 3Pr

  • nPr − 3

  • r ! n − 3Cr − 3

MCQ
Advertisements

उत्तर

r ! n − 3Cr − 3

Here, we have to permute n things of which 3 things are to be included.
So, only the remaining (n - 3) things are left for permutation, taking (r - 3) things at a time. This is because 3 things have already been included.

But, these r things can be arranged in r! ways.
∴ Total number of permutations = r ! n − 3Cr − 3
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 16: Permutations - Exercise 16.7 [पृष्ठ ४६]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 16 Permutations
Exercise 16.7 | Q 1 | पृष्ठ ४६

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Is 3! + 4! = 7!?


How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?


How many 4-digit numbers are there with no digit repeated?


Find n if n – 1P3 : nP4 = 1 : 9


How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?


Which of the following are true:

(2 +3)! = 2! + 3!


Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?


In how many ways can 7 letters be posted in 4 letter boxes?


Evaluate each of the following:

10P

Evaluate each of the following:

P(6, 4)


Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.


Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?


The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is


The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is


How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?


Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.


If (n+2)! = 60[(n–1)!], find n


How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?


How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?


Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.


  1. In how many ways can 8 identical beads be strung on a necklace?
  2. In how many ways can 8 boys form a ring?

Evaluate the following.

`(3! + 1!)/(2^2!)`


The total number of 9 digit number which has all different digit is:


A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?


A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.

How will the answer change if each question may have more than one correct answers?


8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?


In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together


If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY


Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?


How many words can be formed with the letters of the word MANAGEMENT by rearranging them?


In how many ways can 5 children be arranged in a line such that two particular children of them are never together.


The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.


How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if

C1 C2
(a) 4 letters are used at a time (i) 720
(b) All letters are used at a time (ii) 240
(c) All letters are used but the first is a vowel (iii) 360

If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.


If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×